Effects of the quantum interference in collisions of particles have a twofold nature: They arise because of the autocorrelation of a complex scattering amplitude and due to spatial coherence of the incoming wave packets. Both these effects are neglected in a conventional scattering theory dealing with the delocalized plane waves, although they sometimes must be taken into account in particle and atomic physics. Here, we study the role of a transverse coherence length of the packets, putting special emphasis on the case in which one of the particles is twisted, that is, it carries an orbital angular momentum â"â. In ee,ep, and pp collisions the interference results in corrections to the plane-wave cross sections, usually negligible at the energies s≫1 GeV but noticeable for smaller ones, especially if there is a twisted hadron with |â"|>103 in initial state. Beyond the perturbative QCD, these corrections become only moderately attenuated allowing one to probe a phase of the hadronic amplitude as a function of s and t. In this regime, the coherence effects can compete with the loop corrections in QED and facilitate testing the phenomenological models of the strong interaction at intermediate and low energies.